For a short while Anfield felt once again a happy place to be. Liverpool were playing well, winning and threatening to add more goals. There was a good vibe, the sense of a club reminding themselves how enjoyable and satisfying football can be. An array of handsome banners paying homage to Kenny Dalglish swirled on the Kop and, from the man himself, there was the smile that Brian Clough used to say reminded him of everything that was good about the sport.

Yet this was ultimately another day when Dalglish witnessed the shortcomings of his newly inherited team and how far they fall behind the Liverpool sides with which he was once associated. In the space of seven minutes at the start of the second half the hope snapped like a dried twig. Dalglish spent most of the game with his hands pushed deep into the pockets of his overcoat but here, as Everton turned the game upside down with two quick goals, he could be seen holding them out, fingers spread, as if he was struggling to comprehend what he was seeing.

For the man they had come to regale – standing anxiously on the touchline, the worry lines a little more pronounced and the hair a slightly different shade from the last time we saw him mark out his territory – there was at least the sense that this team had the competitive strength and spirit of togetherness to recover from what was a devastating burst of play from David Moyes's side.

Dirk Kuyt's penalty spared Dalglish the ordeal of having to explain a third successive defeat since replacing Roy Hodgson. One draw and two defeats hardly constitutes a new manager's honeymoon period but losing again, particularly to Everton, would have felt like holidaying in a hurricane and there were some encouraging signs to go with the lessons learned about where improvement must be considered mandatory if this team are to climb further away from the ignominy of a relegation battle.

Fernando Torres provided some of the highs and appears to be re-emerging gradually as a footballer capable of menacing the most accomplished of defences. There was an improved performance from Raul Meireles, too, including his first goal for the club (after 33 shots), and Dalglish spoke enthusiastically about the contribution of Martin Kelly, who looks as if he will become a right-back of some distinction.

Even so, Dalglish was pushing the feel-good factor a little too vigorously when he spoke to the media afterwards and adhered to his usual policy of refraining from saying anything even vaguely critical of his team. The returning manager spoke of it being "a very positive day", which was to ignore the erratic defending that had been witnessed at times. Liverpool have not kept a clean sheet in their last six league matches, their vulnerability from crosses encapsulated by Sylvain Distin's goal from a corner.

Dalglish, to give him his due, did concede that Martin Skrtel had been "outmuscled" and it is this area of his team that he needs to regard as a priority now he appears to have coaxed an improvement from Torres. No group of players wants a manager who keeps harping back to the good old days – ie the Graeme Souness syndrome – but Dalglish would be entitled to take his squad through some videos of Liverpool's glory years and remind them that their history of trophies was built on parsimonious defending. Either that or buy a couple of centre-halves and a new left-back.

Torres, though, offers hope – bright, alert and penetrative and playing with a new drive and enthusiasm. That is not to say he is back to being the player who once gave the impression he had the keys to the football universe but there is a considerable improvement from the footballer we have seen at times this season who has looked, in the most difficult moments, as if he did not really want to be there.

The Spaniard flickered only sporadically for Hodgson, his body language dull and tetchy, and in the worst moments he looked as if he had fallen out of love with the sport. What we are seeing now is a player who, once again, seems inspired by his manager. It has become known over the last week as "the Dalglish effect" though, as yet, the results are still very much Hodgsonesque.